Factor models have large potencial in the modeling of several natural and human phenomena. In this paper we consider a multivariate time series \mb{Y}_n, n≥1, rescaled through random factors \mb{T}_n, n≥1, extending some scale mixture models in the literature. We analyze its extremal behavior by deriving the maximum domain of attraction and the multivariate extremal index, which leads to new ways to construct multivariate extreme value distributions. The computation of the multivariate extremal index and the characterization of the tail dependence show the interesting property of these models that however much it is the dependence within and between factors \mb{T}_n, n≥1, the extremal index of the model is unit whenever \mb{Y}_n, n≥1, presents cross-sectional and sequencial tail independence. We illustrate with examples of thinned multivariate time series and multivariate autoregressive processes with random coefficients. An application of these latter to financial data is presented at the end.Helena Ferreira was partially supported by the research unit ``Centro de Matemática" of the University
of Beira Interior and the research project PEst-OE/MAT/UI0212/2014 through the Foundation for Science
and Technology (FCT) co-financed by FEDER/COMPETE.
Marta Ferreira was financed by FEDER Funds through "Programa Operacional Factores de Competitividade - COMPETE" and by Portuguese Funds through FCT - ``Fundação para a Ciência e a Tecnologia", within the project PEst-OE/MAT/UI0013/2014
